A duality between $q$-multiplicities in tensor products and $q$-multiplicities of weights for the root systems $B,C$ or $D$
Résumé
Starting from Jacobi-Trudi's type determinental expressions for the Schur functions of types $B,C$ and $D,$ we define a natural $q$-analogue of the multiplicity $[V(\lambda):M(\mu)]$ when $M(\mu)$ is a tensor product of row or column shaped modules defined by $\mu$. We prove that these $q$-multiplicities are equal to certain Kostka-Foulkes polynomials related to the root systems $C$ or $D$.\ Finally we express the corresponding multiplicities in terms of Kostka numbers
Domaines
Combinatoire [math.CO]
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